# Counting Question

• Mar 7th 2010, 11:52 AM
CoraGB
Counting Question
The textbook we are using in my Discrete class does not have solutions so I was looking for a little bit of help with a problem.

If there are 50 hamburgers at a party with 20 guests, how many ways can the burgers be divided if each person must get at least one, and there may be some hamburgers left over.

Thanks
• Mar 7th 2010, 12:06 PM
Plato
Quote:

Originally Posted by CoraGB
If there are 50 hamburgers at a party with 20 guests, how many ways can the burgers be divided if each person must get at least one, and there may be some hamburgers left over.

We will assume that the hamburgers are considered identical.
Of course the people are all different.
So this question amounts to asking how many ways we can give additional thirty (we have already used up twenty) burgers to twenty people?
The number of ways to put K identical objects into N different cells is $\binom{K+N-1}{K}$.
• Mar 7th 2010, 12:10 PM
CoraGB
Thank you for your response, but the part that I am atuck with is that some burgers may be left over?
• Mar 7th 2010, 12:20 PM
Plato
Quote:

Originally Posted by CoraGB
Thank you for your response, but the part that I am atuck with is that some burgers may be left over?

Try $\binom{30+20}{30}$.
That is like having a twenty-first person that could count as the leftovers.